What is the general solution for 3tan^4(θ)+1= 2/(tan^2(θ)) ?

The general solution for 3tan^4(θ)+1= 2/(tan^2(θ)) is θ=0.71287…+pin,θ=-0.71287…+pin

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3tan^4(θ)+1= 2/(tan^2(θ))

3 tan^{4} (θ) + 1 = \frac{2}{tan ^{2} ( θ )}

θ = 0.71287 \dots + πn, θ = - 0.71287 \dots + πn

Solution steps

3 tan^{4} (θ) + 1 = \frac{2}{tan ^{2} ( θ )}

Solve by substitution

tan (θ) = 0.74741 \dots, tan (θ) = - 0.74741 \dots

tan (θ) = 0.74741 \dots : θ = arctan (0.74741 \dots) + πn

tan (θ) = - 0.74741 \dots : θ = arctan (- 0.74741 \dots) + πn

Combine all the solutions

θ = arctan (0.74741 \dots) + πn, θ = arctan (- 0.74741 \dots) + πn

Show solutions in decimal form

θ = 0.71287 \dots + πn, θ = - 0.71287 \dots + πn

cos^{2} (s) = \frac{3}{4}

tan (\frac{θ}{2} + \frac{π}{4}) = 1, 0 \leq θ \leq 2 π

sin (x + \frac{π}{6}) + sin (x - \frac{π}{6}) = \frac{3}{2}

c, s = \frac{sin ^{2} ( c )}{2}

3 sin^{2} (θ) + 4 cos^{2} (θ) = 4

What is the general solution for 3tan^4(θ)+1= 2/(tan^2(θ)) ?
The general solution for 3tan^4(θ)+1= 2/(tan^2(θ)) is θ=0.71287…+pin,θ=-0.71287…+pin